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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5520.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.f1 | 5520m3 | \([0, -1, 0, -170296, -26932880]\) | \(133345896593725369/340006815000\) | \(1392667914240000\) | \([2]\) | \(46080\) | \(1.7823\) | |
| 5520.f2 | 5520m2 | \([0, -1, 0, -14776, -59024]\) | \(87109155423289/49979073600\) | \(204714285465600\) | \([2, 2]\) | \(23040\) | \(1.4357\) | |
| 5520.f3 | 5520m1 | \([0, -1, 0, -9656, 366960]\) | \(24310870577209/114462720\) | \(468839301120\) | \([2]\) | \(11520\) | \(1.0891\) | \(\Gamma_0(N)\)-optimal |
| 5520.f4 | 5520m4 | \([0, -1, 0, 58824, -530064]\) | \(5495662324535111/3207841648920\) | \(-13139319393976320\) | \([2]\) | \(46080\) | \(1.7823\) |
Rank
sage: E.rank()
The elliptic curves in class 5520.f have rank \(0\).
Complex multiplication
The elliptic curves in class 5520.f do not have complex multiplication.Modular form 5520.2.a.f
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
